Is this company a very famous or desirable place to work? Up-front screening could work very well in that situation. But for less well-known companies like mine, candidates are less willing to go through a lengthy process to interview with us (except the desperate ones, and we don't want those).
I won't do it. That is to say, I won't do it for just any company. I try to determine if a company has their act together by interviewing them back. I don't mind (and expect) some degree of white board coding or something, but there's a level of nuttiness that isn't worth my time for a company that maybe would be good, maybe not. If it's 'just a job' I have other options.
You can get away with more onerous hiring barriers if you pay a better salary or are otherwise a more attractive candidate (top reputation, etc) for employment. If you really are getting much better hires, you should be able to pay better I suppose. I think paying for code samples, or contracting for a few hours of work, etc, are also more respectful ways to get work from a non-employee and signals to the candidate that you're serious and they're at the final step.
Besides, given a population of superstars that want the easiest interview process possible, vs. a population of superstars that want to work with other superstars, which one would you rather work with?
I'd be more concerned with the test not measuring what you want it to measure. It's possible to test well and still not be able to code yourself out of a paper bag, and it's possible (though somewhat less likely) to code well and not test well.